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+(* -*- coq-prog-args: ("-emacs-U") -*- *)
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+(* Custom notations and implicits for Coq prelude definitions.
+ *
+ * Author: Matthieu Sozeau
+ * Institution: LRI, CNRS UMR 8623 - UniversitÃcopyright Paris Sud
+ *              91405 Orsay, France *)
+
+(** Notations for the unit type and value. *)
+
+Notation " () " := Datatypes.unit : type_scope.
+Notation " () " := tt.
+
+(** Set maximally inserted implicit arguments for standard definitions. *)
+
+Implicit Arguments eq [[A]].
+
+Implicit Arguments Some [[A]].
+Implicit Arguments None [[A]].
+
+Implicit Arguments inl [[A] [B]].
+Implicit Arguments inr [[A] [B]].
+
+Implicit Arguments left [[A] [B]].
+Implicit Arguments right [[A] [B]].
+
+Require Import Coq.Lists.List.
+
+Implicit Arguments nil [[A]].
+Implicit Arguments cons [[A]].
+
+(** Standard notations for lists. *)
+
+Notation " [ ] " := nil : list_scope.
+Notation " [ x ] " := (cons x nil) : list_scope.
+Notation " [ x ; .. ; y ] " := (cons x .. (cons y nil) ..) : list_scope.
+
+(** n-ary exists *)
+
+Notation " 'exists' x y , p" := (ex (fun x => (ex (fun y => p))))
+  (at level 200, x ident, y ident, right associativity) : type_scope.
+
+Notation " 'exists' x y z , p" := (ex (fun x => (ex (fun y => (ex (fun z => p))))))
+  (at level 200, x ident, y ident, z ident, right associativity) : type_scope.
+
+Notation " 'exists' x y z w , p" := (ex (fun x => (ex (fun y => (ex (fun z => (ex (fun w => p))))))))
+  (at level 200, x ident, y ident, z ident, w ident, right associativity) : type_scope.
+
+Tactic Notation "exist" constr(x) := exists x.
+Tactic Notation "exist" constr(x) constr(y) := exists x ; exists y.
+Tactic Notation "exist" constr(x) constr(y) constr(z) := exists x ; exists y ; exists z.
+Tactic Notation "exist" constr(x) constr(y) constr(z) constr(w) := exists x ; exists y ; exists z ; exists w.